LECTURE 3 PARTICLE INTERACTIONS & FEYNMAN DIAGRAMS PHY492 Nuclear and Elementary Particle Physics

LECTURE 3
PARTICLE INTERACTIONS &
FEYNMAN DIAGRAMS
PHY492 Nuclear and Elementary Particle Physics
Last Lecture
Any differentiable symmetry
of the action of a physical system
has a corresponding conservation law. Emmy Noether
(1882-1935) Rotational symmetry Angular momemtum conservation Transitional symmetry Momemtum conservation Time symmetry Energy conservation January 10, 2014 9:10am January 9 PHY492, Lecture 3 9:50am January 9 2 Interactions
In the context of symmetries, we saw that a particle (field) could interact
with a Hamiltonian.
Consider the Coulomb potential in which charged particles interact.
Two major concepts associated with interactions:
1)  The interaction represents the expression of a potential acting on the field.
IE, the Hamiltonian has the form H=T+V where V is non-zero.
2)  This potential implies a force, and in quantum field theory, we manifest this
force through the exchange of force carriers.
January 10, 2014 PHY492, Lecture 3 3 Feynman Diagrams
Space Time h:p://en.wikipedia.org/wiki/Fundamental_interacGon January 10, 2014 PHY492, Lecture 3 4 Feynman Diagrams (2)
fermion line (eg, an electron or quark) anG-­‐fermion line (eg, a positron or anG-­‐quark) scalar line (eg, a Higgs boson) gluon line gauge boson line (eg, photon or Z boson) January 10, 2014 PHY492, Lecture 3 5 Feynman Diagrams (2)
People don’t always follow the rules!
January 10, 2014 PHY492, Lecture 3 6 Feynman Rules
Rules for Feynman Diagrams
1. 
Initial state (left) and final state (right)
2. 
Lines are defined as on slide 6
3. 
Arrowhead pointing to the right (left) indicate particles (anti-particles)
Arrows do not indicate the particle’s direction of motion!
4. 
Lines that end at boundaries are free particles
5. 
Vertices represent particle interactions
5a. Energy (or momentum) is conserved at a vertex
5b. Charge is conserved at a vertex
e- e- 5c. Fermion number is conserved at a vertex
5d. Quark number is conserved at a vertex
6. 
A rotation of a Feynman diagram must result in
a valid diagram.
7. 
Internal propagator lines may not satisfy normal
relativistic mass-energy relationships.
January 11, 0, 2012 014 PHY492, Lecture 2
3 γ e- e- 7 Feynman Diagrams (3)
January 10, 2014 PHY492, Lecture 3 8 Feynman Diagrams (3)
Examples: January 10, 2014 PHY492, Lecture 3 9 Feynman Diagrams (4)
More Examples: January 10, 2014 PHY492, Lecture 3 10 Feynman Diagrams (5)
Representations of
neutron beta decay January 10, 2014 PHY492, Lecture 3 11 Feynman Diagrams (6)
January 10, 2014 PHY492, Lecture 3 12 Calculations
Feynman diagrams are useful visualization tools, but they were invented to help
perform calculations!
Feynman diagrams encode the information needed to calculate things like
interaction probabilities, differential kinematic distributions, etc.
Par,cle 4-­‐momentum Nature of Propagator Force Strong ElectromagneGc Weak January 10, 2014 Rela,ve Strength 1 1/137 Interac,on Strength 10-­‐6 PHY492, Lecture 3 13 Virtual Particles
Quantum mechanics allows for a very interesting effect for the lifetime and
behavior of particles.
Consider Heisenberg's uncertainty principle:
ΔEΔt ≥ !
Propagators might not satisfy the normal energy-mass relationship:
2
m2 = E 2 − p2
Any particle that violates this relationship (off mass shell) is referred to as a virtual
particle.
•  Virtual particles may have zero or even negative “mass”.
•  Virtual particles don’t manifest in reality, so they can only be internal lines
A consequence: Coulomb forces and magnetic fields exist due to the exchange of
virtual photons.
January 10, 2014 PHY492, Lecture 3 14